Tony Ware

Research

Mathematical finance, scientific computation and numerical analysis - in particular

Numerical methods for financial derivative pricing.
Models for natural gas and electricity markets.
Portfolio optimisation with quantile-based risk measures.
Adaptive wavelet approximation of functions and operators.
Wavelet-based analysis of biomedical signals.

Selected publications, working papers and talks.

Tony Ware 2005

Swing options in a mean-reverting world [pdf]

Slides from a talk presented at "Stochastic Calculus and its applications to Quantitative Finance and Electrical Engineering", a conference in honour of Robert Elliott, Calgary, 24-27 July 2005.

Abstract Swing options can be seen as generalisations of American or bermudan options that give the holder a certain constrained freedom to exercise partially at some discrete set of times, or indeed to exercise continuously at some rate of their choosing. In this way they are closely related to passport options. They are used in the energy industry to value natural gas storage facilities and power delivery contracts. Elliott and Cadenillas address the question of pricing swing options for log-normal and mean-reverting assets, describing conditions under which they reduce to American options and also describing a set of variational inequalities that serve to define the solution in more general settings. In this paper we develop a finite-element approach to this class of problems which can be applied in the presence of strong mean-reversion in the underlying prices. We explore the continuous-time limit under various types of exercise constraint, while addressing issues of accuracy and computational complexity.

Len Bos, Tony Ware and Boris Pavlov 2002

On a semi-spectral method for pricing an option on a mean-reverting asset [web]

Quantitative Finance, Volume 2, pp. 337-345

Abstract We consider a risky asset following a mean-reverting stochastic process of the form $dS = \alpha (L-S) dt + \sigma S dW$. We show that the (singular) diffusion equation which gives the value of a European option on S can be represented, upon expanding in Laguerre polynomials, by a tridiagonal infinite matrix. We analyse this matrix to show that the diffusion equation does indeed have a solution and truncate the matrix to give a simple, highly efficient method for the numerical calculation of the solution.

Len Bos and Tony Ware 2001

How to solve multi-asset Black-Scholes with time-dependent volatility and correlation

Journal of Computational Finance, 4(2):99--107, Winter 2001

Ali Lari-Lavassani Mohammedreza Simchi and Tony Ware 2001

A discrete valuation of swing options [pdf]

Canadian Applied Mathematics Quarterly, 9(1):35--74, Spring 2001

Abstract A discrete forest methodology is developed for swing options as a dynamically coupled system of European options. Numerical implementation is fully developed for one- and two-factor, mean-reverting, underlying processes, with application to energy markets. Convergence is established via finite difference methods. Qualitative properties and sensitivity analysis are considered.

Ali Lari-Lavassani, Ali A. Sadeghi and Tony Ware 2001

Modelling and implementing mean reverting price processes in energy markets [pdf]

Electronic Publications of the International Energy Credit Association (www.ieca.net).

Abstract Various one to three factor mean reverting processes are investigated in the context of energy markets. Results of natural gas and crude oil market data calibrations are presented. Numerical implementations of the multifactor models are discussed via binomial trees, a finite difference method and Monte Carlo simulation.

Here is more-or-less up to date list of my papers and technical reports.

Tony Ware

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Research


Tony Ware	2005
Swing options in a mean-reverting world	[pdf]
Slides from a talk presented at "Stochastic Calculus and its applications to Quantitative Finance and Electrical Engineering", a conference in honour of Robert Elliott, Calgary, 24-27 July 2005.
Abstract Swing options can be seen as generalisations of American or bermudan options that give the holder a certain constrained freedom to exercise partially at some discrete set of times, or indeed to exercise continuously at some rate of their choosing. In this way they are closely related to passport options. They are used in the energy industry to value natural gas storage facilities and power delivery contracts. Elliott and Cadenillas address the question of pricing swing options for log-normal and mean-reverting assets, describing conditions under which they reduce to American options and also describing a set of variational inequalities that serve to define the solution in more general settings. In this paper we develop a finite-element approach to this class of problems which can be applied in the presence of strong mean-reversion in the underlying prices. We explore the continuous-time limit under various types of exercise constraint, while addressing issues of accuracy and computational complexity.

Len Bos, Tony Ware and Boris Pavlov	2002
On a semi-spectral method for pricing an option on a mean-reverting asset	[web]
Quantitative Finance, Volume 2, pp. 337-345
Abstract We consider a risky asset following a mean-reverting stochastic process of the form $dS = \alpha (L-S) dt + \sigma S dW$. We show that the (singular) diffusion equation which gives the value of a European option on S can be represented, upon expanding in Laguerre polynomials, by a tridiagonal infinite matrix. We analyse this matrix to show that the diffusion equation does indeed have a solution and truncate the matrix to give a simple, highly efficient method for the numerical calculation of the solution.

Len Bos and Tony Ware	2001
How to solve multi-asset Black-Scholes with time-dependent volatility and correlation
Journal of Computational Finance, 4(2):99--107, Winter 2001

Ali Lari-Lavassani Mohammedreza Simchi and Tony Ware	2001
A discrete valuation of swing options	[pdf]
Canadian Applied Mathematics Quarterly, 9(1):35--74, Spring 2001
Abstract A discrete forest methodology is developed for swing options as a dynamically coupled system of European options. Numerical implementation is fully developed for one- and two-factor, mean-reverting, underlying processes, with application to energy markets. Convergence is established via finite difference methods. Qualitative properties and sensitivity analysis are considered.

Ali Lari-Lavassani, Ali A. Sadeghi and Tony Ware	2001
Modelling and implementing mean reverting price processes in energy markets	[pdf]
Electronic Publications of the International Energy Credit Association (www.ieca.net).
Abstract Various one to three factor mean reverting processes are investigated in the context of energy markets. Results of natural gas and crude oil market data calibrations are presented. Numerical implementations of the multifactor models are discussed via binomial trees, a finite difference method and Monte Carlo simulation.